The only carrier variant ATM is Verizon, and the downside is that the Bootloader is locked, which means that you can't root the device.
As far as updates go, Google releases all of the updates directly (ie none come from Verizon). That's not to say that there haven't been delays in the past in releasing builds for the carrier variant - it happened several times for the Nexus 6P (my previous phone), where a build was released for the unlocked device and it took some time to before the Verizon build was posted. YMMV.